IRR Calculator

What the internal rate of return is

The internal rate of return (IRR) is the single yearly rate that makes the present value of an investment's future cash flows equal to its cost. Put differently, it is the discount rate at which the net present value is exactly zero. If you could earn the IRR on your money each year, you would end up in the same place as the project does.

Because the answer is a percentage, IRR lets you compare projects of different sizes and lengths on one scale, and you can set it against a required return or the cost of capital (see the WACC calculator). A project is normally worth considering when its IRR is above that hurdle.

How to use the calculator

• Initial investment: the money you pay at the start, as a positive number of at least 1.
• How many years?: a whole number from 2 to 25. A box appears for each year.
• Year 1, Year 2, ...: the net cash flow you receive (positive) or pay (negative) at the end of each year. A blank box counts as zero.

Cash flows are read as whole dollars, so any cents you type are dropped. At least one cash flow must be positive, otherwise there is nothing to earn a return from and the calculator asks for one.

Besides the IRR, you get the gross return, which is total cash received minus the investment, divided by the investment, and the net cash flow, the same difference in dollars. Neither of those two figures accounts for timing; only the IRR does.

The IRR formula

With initial investment C₀ and cash flows CF₁ to CFₙ at the end of years 1 to n, the IRR is the rate r that satisfies:

0 = −C₀ + CF₁ ÷ (1 + r)¹ + CF₂ ÷ (1 + r)² + … + CFₙ ÷ (1 + r)ⁿ

There is no way to isolate r algebraically once there are more than a few periods, so the calculation is done numerically. The idea is simple: try a rate, see whether the net present value comes out positive or negative, and narrow the range until the value is as close to zero as the arithmetic allows.

Worked example

A project costs $1,000 and returns $200, $300, $400, $300 and $200 over five years. The net present value at three trial rates is:

The sign flips between 12% and 13%, so the IRR lies there. Refining the search gives 12.261%. You can confirm it by discounting each cash flow at that rate:

The present values add up to the $1,000 invested, which is exactly what the IRR means. The gross return is (1,400 − 1,000) ÷ 1,000 = 40%, and the net cash flow is $400. Notice how much smaller the 12.261% yearly figure is than the 40% gross return: the gross figure ignores that the money comes back over five years.

Using the IRR to make a decision

Take a project that costs $50,000 and pays $12,000, $15,000, $18,000 and $20,000 over four years. Its IRR is about 10.415%. Whether that is good depends on your hurdle rate: discounted at 8%, the project has a net present value of +$2,960.77 and clears the bar; at 10% it is still slightly positive (+$489.72); at 12% it is negative (−$1,805.40) and should be rejected.

When choosing between several projects, compare their IRRs but also their net present values. A smaller project can post a higher IRR while adding less total value than a bigger one.

Limits and pitfalls

• Several IRRs. If the cash flows change sign more than once, the equation can have more than one solution. An investment of $1,000 followed by +$3,600 and then −$2,800, for instance, breaks even at both 13.67% and 146.33%. The calculator reports one figure, so check the net present value at a few rates when your cash flows swing between positive and negative.
• Reinvestment assumption. IRR implicitly assumes cash received along the way can be reinvested at the IRR itself, which is optimistic for high-return projects.
• Yearly, evenly spaced cash flows only. For payments on specific dates use the XIRR calculator.
• Search range. The search covers rates from about −99% up to 1,260% a year. If the true rate is higher, the result shows 1,260%; if there is no break-even rate in the range, you will see −607.5%.

IRR is a model result, not a forecast or advice. Check your inputs and consider taxes, risk and fees. See our disclaimer.